Variational Models and Methods in Solid and Fluid Mechanics [electronic resource] /
International Centre for Mechanical Sciences.
dell'Isola, Francesco.editor.
Gavrilyuk, Sergey.editor.
Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Description based upon print version of record.
""Title Page ""; ""Copyright Page ""; ""PREFACE""; ""Table of Contents""; ""Variational principles are a powerful tool also for formulating field theories""; ""1 Introduction and historical background""; ""1.1 Metrodoron and his followers""; ""1.2 Why Variational Principles and Calculus of Variation?""; ""1.3 The problem of including dissipation""; ""2 Finding a mathematical model for natural phenomena""; ""2.1 Principle of Least Action""; ""2.2 The Rayleigh-Hamilton principle""; ""2.3 La Cin`ematique dâ€?Abord !""; ""2.4 La Nature agit toujours par les voies les plus simples""
""2.5 Two possible choices for the set of admissible and accessible motions""""2.6 Further famous quotes""; ""3 In other words: How to find â€œReal Motionsâ€??""; ""4 Lagrangian Action Functionals: technical details""; ""4.1 Variation of the Action Functional""; ""4.2 The Space-Time Case (m = 4)""; ""5 Principle of Virtual Power and Principle of Least Action""; ""6 Hamilton-Rayleigh Approach""; ""7 Conclusions""; ""Bibliography""; ""Beyond Euler-Cauchy Continua: The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument.""
""1 Introduction""""2 Second and Higher Gradient Continuum Theories""; ""2.1 A first method for extending Cauchy model for continuous bodies""; ""2.2 A second method for extending Cauchy model and its relationship with the first""; ""The mathematical difficulties presented by this second method""; ""2.3 The two methods can be reconciled.""; ""3 Some commentaries about a recent paper on second gradient continua""; ""3.1 Concluding remarks""; ""4 ResumÂ?e of some results in Differential Geometry of Riemannian manifolds embedded in the Euclidean Space.""
""5 Gaussian Geometry of Piecewise Regular Surfaces in E3""""5.1 Piecewise regular surfaces embedded in E3.""; ""5.2 Local parametrizations for regular curves and surfaces. Local curvilinear coordinate systems in E3 adapted to surfaces and surface edges.""; ""6 Gauss Divergence Theorem for embedded Riemannian manifolds""; ""7 Power expended by internal or external actions""; ""7.1 Representations of distributions which are Nâ??th order derivatives of absolutely continuous measures concentrated on submanifolds of RH with border""
""8 Principle of Virtual Powers applied to N â?? th gradient continua.""""9 Contact actions in N â?? th order strain-gradient multipolar continua: N â?? th order forces and stress multipoles.""; ""9.1 The terms of surface (1-)forces and surface L + 1â?? forces""; ""9.2 The terms of line (1-)forces and line J + 1â?? forces.""; ""9.3 The terms of (1-)forces and J + 1â?? forces concentrated on wedges""; ""9.4 The obtained expression for Internal Power in N â??th Gradient Continua""; ""9.5 Some final considerations about obtained results:""; ""10 Bodies, Contact Surfaces and Shapes ??""
""10.1 Contact Actions""
Includes bibliographical references.
Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Mechanics.
Mechanics, Applied.
Calculus of variations.
Theoretical and Applied Mechanics.
Calculus of Variations and Optimal Control; Optimization.
Classical Mechanics.


CISM International Centre for Mechanical Sciences